Functions-10

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Is g = {(1,1), (2,3), (3,5), (4,7)} a function? If this is described by the formula, g(x) = αx + β,
then what values should be assigned to α and β?

Solution: Since no two ordered pairs in g have the same first component, so, g is a function such that g(1) = 1, g(2) = 3 and

g(3) = 5 and g(4) = 7.

It is given that g(x) = αx + β. Therefore,

g(1) = 1 and g(2) = 3 => α + β = 1 and 2α + β = 3 => α = 2, β = -1.

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